First four terms are 7, -13, 67, -253
Solution:
Given that,
[tex]f(1) = 7[/tex]
The formula to find nth term is given as:
[tex]f(n) = -4 \times f(n-1) + 15[/tex]
We can find the first four terms by substituting n = 2, 3, 4
First term:
f(1) = 7
Second term:
Substitute n = 2
[tex]f(2) = -4 \times f(2-1) + 15\\\\f(2) = -4 \times f(1) + 15\\\\Substitute\ f(1) = 7\\\\f(2) = -4 \times 7 + 15\\\\Simplify\\\\f(2) = -28 + 15\\\\f(2) = -13[/tex]
Third term:
Substitute n = 3
[tex]f(3) = -4 \times f(3-1) + 15\\\\f(3) = -4 \times f(2) + 15\\\\Substitute\ f(2) = -13\\\\f(3) = -4 \times -13 + 15\\\\Simplify\\\\f(3) = 52+15\\\\f(3) = 67[/tex]
Fourth term:
Substitute n = 4
[tex]f(4) = -4 \times f(4-1) + 15\\\\f(4) = -4 \times f(3) + 15\\\\Substitute\ f(3) = 67\\\\f(4) = -4 \times 67 + 15\\\\Simplify\\\\f(4) = -268+15\\\\f(4) = -253[/tex]
Thus first four terms are 7, -13, 67, -253
